In place of flour and leaveners, whipped eggs whites to produce cupcakes with a light-as-air texture.
Preheat oven to 275 degrees. Line standard muffin tins with paper liners. Melt butter and chocolate in a large heatproof bowl set over (not in) a pan of simmering water. Stir to combine, then remove bowl from heat and let cool slightly. Whisk in egg yolks.
With an electric mixer on medium speed, whisk egg whites until soft peaks form. Gradually add sugar, beating until peaks are stiff and glossy but not dry (do not overbeat). Whisk one quarter of the beaten egg whites into chocolate mixture to lighten; gently fold mixture into remaining whites.
Divide batter evenly among lined cups, filling each three-quarters full. Bake, rotating tins halfway through, until cupcakes are just set in centers, about 25 minutes. Transfer tins to wire racks to cool completely before removing cupcakes (their centers will sink). Cupcakes are best eaten the same day they are baked; keep at room temperature until ready to serve, topped with scoops of ice cream, if desired.